Source: http://www.abarim-publications.com/DictionaryG/e/e-u.html

ευ

The familiar adverb ευ (eu) means good or noble. It's used in constructions like "that it may be well with you" (Ephesians 6:3), or "well done!" (Luke 19:17). But mostly our word is used as a prefix to an extensive array of nouns and verbs, sometimes to distinguish a regular item from an outstanding version of it, but mostly as an intensitive. It survives in English in words like Eucharist and Euchologion (an Orthodox book of prayer), or even euphoria, euphemism, eucalyptus, eunomia and others.